An energy storage apparatus for an onboard electrical system of a motor vehicle has a first electrical energy store characterized by a first voltage characteristic curve defining the quiescent voltage of the first store depending on the relative state of charge of the first store, and a second electrical energy store which can be connected in parallel with the first electrical energy store by a controllable switching element and which is characterized by a second voltage characteristic curve defining the quiescent voltage of the second electrical energy store depending on the relative state of charge of the second store. A first voltage value range covered by the first voltage characteristic curve and a second voltage value range which is covered by the second voltage characteristic curve partially overlap. The energy storage apparatus further has a device for determining the state of charge of the first energy store and/or of the second energy store. The device establishes the state of charge either by a quiescent voltage measurement device or by a state of charge determination device by balancing a respective battery current. The device opens the controllable switching element when the motor vehicle is in a state similar to the quiescent state and a quality value determined during a previous state of charge determination process in parallel with the state of charge and expressing the quality of the balancing exceeds a predefined threshold value. When the two criteria are fulfilled, the quiescent voltage measurement device for determining the state of charge of at least the first energy store is activated.